I have encountered "Thou hast said" number of times in the N.T. Perhaps, it can also be found in O.T. I wonder if it is absolutely synonymous to "yes" or it is a way of implying "yes" while not actually saying it (perhaps, for reasons of avoiding responsibility)?

Matthew 26:64:

Jesus saith unto him, Thou hast said: nevertheless I say unto you,
Hereafter shall ye see the Son of man sitting on the right hand of
power, and coming in the clouds of heaven.

In some contexts used it can be construed to mean - so says you, an acknowledgment that a person's viewpoint frames their reality, while not ascribing to that view. It can be a kind way to say I don't agree, but as long as you think it, it will manifest itself as truth and you will find multiple "proofs" to reinforce that idea. Much of human reasoning is re-affirmational (confirmation bias) and bandwagoning bad ideas, thus bringing an element of reality to them, Jesus as Christ being a good example of how these proclivities of thought tend to compound on themselves in a form of thermal runaway.

Many times Jesus's response in this manner reveals his ideology that what you think, and how you judge determines the reality that you will personally live. He also used this response as a means to weasel out of proclaiming himself divine or titled and getting into trouble. "So Pilate asked him, "Are you the king of the Jews?" Jesus replied, "You have said it." Luke 23:3